202:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Integración:@0.073089:0.043661:0.176062:0.043661:0.176062:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dada la derivada ( ) '( ) de una función definida en algún:@0.323781:0.447360:0.794227:0.447360:0.794227:0.431648:0.323781:0.431648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dg:@0.449290:0.439792:0.465940:0.439792:0.465940:0.425760:0.449290:0.425760:0.000000:0.000000 dx:@0.450010:0.456182:0.465204:0.456182:0.465204:0.442150:0.450010:0.442150:0.000000:0.000000 x:@0.471161:0.447360:0.478616:0.447360:0.478616:0.431925:0.471161:0.431925:0.000000 5:@0.487286:0.446806:0.502619:0.446806:0.502619:0.433090:0.487286:0.433090:0.000000 g x:@0.506485:0.447360:0.531114:0.447360:0.531114:0.431925:0.506485:0.431925:0.000000:0.000000:0.000000 g:@0.653798:0.447360:0.663057:0.447360:0.663057:0.431925:0.653798:0.431925:0.000000 subconjunto de , ¿cómo podemos recuperar la función ?:@0.323756:0.487079:0.770113:0.487079:0.770113:0.471366:0.323756:0.471366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.420431:0.487079:0.430316:0.487079:0.430316:0.471643:0.420431:0.471643:0.000000 R:@0.456914:0.486219:0.470204:0.486219:0.470204:0.473322:0.456914:0.473322:0.000000 g:@0.753915:0.487079:0.763174:0.487079:0.763174:0.471643:0.753915:0.471643:0.000000 La definición de primitiva (llamada también integral indefinida de una función ) :@0.323738:0.526797:0.930901:0.526797:0.930901:0.511085:0.323738:0.511085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.917206:0.526797:0.921900:0.526797:0.921900:0.511362:0.917206:0.511362:0.000000 responde en parte a esta pregunta. Para simplificar la exposición, asumimos que :@0.323738:0.545076:0.930901:0.545076:0.930901:0.529363:0.323738:0.529363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.323738:0.563354:0.333622:0.563354:0.333622:0.547919:0.323738:0.547919:0.000000 , . En realidad, este conjunto pueden ser conjuntos:@0.333549:0.563354:0.761363:0.563354:0.761363:0.547641:0.333549:0.547641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.337506:0.562799:0.352839:0.562799:0.352839:0.549083:0.337506:0.549083:0.000000 F:@0.356705:0.563936:0.360791:0.563936:0.360791:0.546282:0.356705:0.546282:0.000000 a b:@0.360699:0.563354:0.386212:0.563354:0.386212:0.547919:0.360699:0.547919:0.000000:0.000000:0.000000 G:@0.386138:0.563936:0.390225:0.563936:0.390225:0.546282:0.386138:0.546282:0.000000 A:@0.588360:0.563354:0.598245:0.563354:0.598245:0.547919:0.588360:0.547919:0.000000 G:@0.484046:0.603655:0.488133:0.603655:0.488133:0.586001:0.484046:0.586001:0.000000 2`:@0.488041:0.602518:0.515560:0.602518:0.515560:0.588802:0.488041:0.588802:0.000000:0.000000 , , , , :@0.515468:0.603072:0.622708:0.603072:0.622708:0.587360:0.515468:0.587360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a a:@0.522536:0.603072:0.556037:0.603072:0.556037:0.587637:0.522536:0.587637:0.000000:0.000000:0.000000 F G:@0.531721:0.603655:0.546870:0.603655:0.546870:0.586001:0.531721:0.586001:0.000000:0.000000:0.000000 `:@0.563032:0.602518:0.575310:0.602518:0.575310:0.588802:0.563032:0.588802:0.000000 F:@0.575217:0.603655:0.579304:0.603655:0.579304:0.586001:0.575217:0.586001:0.000000 R:@0.586280:0.602213:0.599570:0.602213:0.599570:0.589315:0.586280:0.589315:0.000000 5 2` `:@0.603436:0.602518:0.673402:0.602518:0.673402:0.588802:0.603436:0.588802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G:@0.622635:0.603655:0.626721:0.603655:0.626721:0.586001:0.622635:0.586001:0.000000 , , entre otros.:@0.654056:0.603072:0.766598:0.603072:0.766598:0.587360:0.654056:0.587360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F:@0.673310:0.603655:0.677396:0.603655:0.677396:0.586001:0.673310:0.586001:0.000000 Definición:@0.293586:0.642791:0.371554:0.642791:0.371554:0.626121:0.293586:0.626121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.293586:0.682509:0.297397:0.682509:0.297397:0.665562:0.293586:0.665562:0.000000 Una función se dice integral indefinida de una función real en un intervalo abierto , :@0.297047:0.682509:0.930846:0.682509:0.930846:0.666797:0.297047:0.666797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.389507:0.682509:0.398269:0.682509:0.398269:0.667074:0.389507:0.667074:0.000000 f:@0.733501:0.682509:0.738195:0.682509:0.738195:0.667074:0.733501:0.667074:0.000000 G:@0.910432:0.683092:0.914518:0.683092:0.914518:0.665438:0.910432:0.665438:0.000000 a:@0.914426:0.682509:0.923685:0.682509:0.923685:0.667074:0.914426:0.667074:0.000000 b:@0.293568:0.700788:0.302827:0.700788:0.302827:0.685352:0.293568:0.685352:0.000000 F:@0.302753:0.701370:0.306840:0.701370:0.306840:0.683716:0.302753:0.683716:0.000000 de , si y solo si verifica: :@0.306748:0.700788:0.499678:0.700788:0.499678:0.685075:0.306748:0.685075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.333420:0.699928:0.346710:0.699928:0.346710:0.687030:0.333420:0.687030:0.000000 P:@0.428641:0.700788:0.437402:0.700788:0.437402:0.685352:0.428641:0.685352:0.000000 dP:@0.528485:0.732974:0.544683:0.732974:0.544683:0.718942:0.528485:0.718942:0.000000:0.000000 dx:@0.528987:0.749364:0.544181:0.749364:0.544181:0.735332:0.528987:0.735332:0.000000:0.000000 ( ) ( ), :@0.545326:0.740543:0.614224:0.740543:0.614224:0.724830:0.545326:0.724830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.550130:0.740543:0.557585:0.740543:0.557585:0.725107:0.550130:0.725107:0.000000 5:@0.566255:0.739988:0.581588:0.739988:0.581588:0.726272:0.566255:0.726272:0.000000 f x:@0.585454:0.740543:0.602333:0.740543:0.602333:0.725107:0.585454:0.725107:0.000000:0.000000:0.000000 ;:@0.614132:0.739988:0.626410:0.739988:0.626410:0.726272:0.614132:0.726272:0.000000 x:@0.626318:0.740543:0.633773:0.740543:0.633773:0.725107:0.626318:0.725107:0.000000 , .:@0.633699:0.740543:0.692796:0.740543:0.692796:0.724830:0.633699:0.724830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.637660:0.740253:0.652296:0.740253:0.652296:0.726843:0.637660:0.726843:0.000000 G:@0.656166:0.741125:0.660252:0.741125:0.660252:0.723471:0.656166:0.723471:0.000000 a b:@0.660160:0.740543:0.685673:0.740543:0.685673:0.725107:0.660160:0.725107:0.000000:0.000000:0.000000 F:@0.685599:0.741125:0.689685:0.741125:0.689685:0.723471:0.685599:0.723471:0.000000 A la integral indefinida también se denomina :@0.293653:0.780261:0.645606:0.780261:0.645606:0.764549:0.293653:0.764549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 antiderivada:@0.647220:0.780261:0.745776:0.780261:0.745776:0.763592:0.647220:0.763592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 o :@0.745993:0.780261:0.765726:0.780261:0.765726:0.764549:0.745993:0.764549:0.000000:0.000000:0.000000 primitiva:@0.767401:0.780261:0.837610:0.780261:0.837610:0.763592:0.767401:0.763592:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . La integral :@0.837809:0.780261:0.930867:0.780261:0.930867:0.764549:0.837809:0.764549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 indefinida de una función dada no es única.:@0.293635:0.798540:0.610737:0.798540:0.610737:0.782827:0.293635:0.782827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Se representa con el símbolo ( ) que se lee “integral indefinida:@0.293635:0.838258:0.771255:0.838258:0.771255:0.822545:0.293635:0.822545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.507325:0.838840:0.516528:0.838840:0.516528:0.821186:0.507325:0.821186:0.000000 f x dx:@0.516436:0.838258:0.554687:0.838258:0.554687:0.822823:0.516436:0.822823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ( ) \. En la integración el símbolo ( ) que tiene la forma de la letra mayúscula :@0.293635:0.877977:0.930960:0.877977:0.930960:0.862264:0.293635:0.862264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x dx:@0.316718:0.877977:0.354968:0.877977:0.354968:0.862541:0.316718:0.862541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.572045:0.878559:0.581248:0.878559:0.581248:0.860905:0.572045:0.860905:0.000000 f x dx:@0.581156:0.877977:0.619407:0.877977:0.619407:0.862541:0.581156:0.862541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.836925:0.877977:0.844987:0.877977:0.844987:0.862541:0.836925:0.862541:0.000000 estirada, denota o indica suma. Se tiene::@0.293635:0.896255:0.583431:0.896255:0.583431:0.880542:0.293635:0.880542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e:@0.503956:0.936556:0.513160:0.936556:0.513160:0.918902:0.503956:0.918902:0.000000 f x dx:@0.513068:0.935973:0.551318:0.935973:0.551318:0.920538:0.513068:0.920538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) ( ) , :@0.517688:0.935973:0.637980:0.935973:0.637980:0.920261:0.517688:0.920261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.555221:0.935419:0.570554:0.935419:0.570554:0.921703:0.555221:0.921703:0.000000 P x:@0.574419:0.935973:0.595367:0.935973:0.595367:0.920538:0.574419:0.920538:0.000000:0.000000:0.000000 1:@0.604037:0.935419:0.619370:0.935419:0.619370:0.921703:0.604037:0.921703:0.000000 c:@0.623235:0.935973:0.630893:0.935973:0.630893:0.920538:0.623235:0.920538:0.000000 ;:@0.637887:0.935419:0.650165:0.935419:0.650165:0.921703:0.637887:0.921703:0.000000 x:@0.650073:0.935973:0.657528:0.935973:0.657528:0.920538:0.650073:0.920538:0.000000 , ,:@0.657454:0.935973:0.716575:0.935998:0.716575:0.920285:0.657454:0.920261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.661439:0.935708:0.676075:0.935708:0.676075:0.922298:0.661439:0.922298:0.000000 F:@0.679945:0.936580:0.684031:0.936580:0.684031:0.918926:0.679945:0.918926:0.000000 a b:@0.683939:0.935998:0.709452:0.935998:0.709452:0.920563:0.683939:0.920563:0.000000:0.000000:0.000000 G:@0.709378:0.936580:0.713464:0.936580:0.713464:0.918926:0.709378:0.918926:0.000000 Integrar:@0.082576:0.187325:0.131986:0.187325:0.131986:0.173687:0.082576:0.173687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es el proceso :@0.131915:0.187325:0.215991:0.187325:0.215991:0.174469:0.131915:0.174469:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 recíproco del de :@0.082576:0.200941:0.182461:0.200941:0.182461:0.188086:0.082576:0.188086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 derivar:@0.182307:0.200941:0.225854:0.200941:0.225854:0.187303:0.182307:0.187303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Es :@0.225771:0.200941:0.247444:0.200941:0.247444:0.188086:0.225771:0.188086:0.000000:0.000000:0.000000:0.000000:0.000000 decir, dada una función ( ), :@0.082561:0.214557:0.248453:0.214557:0.248453:0.201702:0.082561:0.201702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.224853:0.214557:0.238663:0.214557:0.238663:0.201928:0.224853:0.201928:0.000000:0.000000:0.000000 busca aquellas funciones :@0.082561:0.228173:0.234582:0.228173:0.234582:0.215318:0.082561:0.215318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F x:@0.082561:0.241789:0.099113:0.241789:0.099113:0.229161:0.082561:0.229161:0.000000:0.000000:0.000000 ( ) que, al ser derivadas, :@0.089083:0.241789:0.231401:0.241789:0.231401:0.228934:0.089083:0.228934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conducen a ( ).:@0.082561:0.255406:0.176659:0.255406:0.176659:0.242550:0.082561:0.242550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.156358:0.255406:0.170168:0.255406:0.170168:0.242777:0.156358:0.242777:0.000000:0.000000:0.000000 Se dice, entonces, que ( ) es :@0.082561:0.272596:0.257835:0.272596:0.257835:0.259740:0.082561:0.259740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F x:@0.218015:0.272596:0.234567:0.272596:0.234567:0.259967:0.218015:0.259967:0.000000:0.000000:0.000000 una primitiva o antiderivada :@0.082546:0.286212:0.252538:0.286212:0.252538:0.273356:0.082546:0.273356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ( ); dicho de otro modo, :@0.082546:0.299828:0.250218:0.299828:0.250218:0.286972:0.082546:0.286972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.101146:0.299828:0.114956:0.299828:0.114956:0.287199:0.101146:0.287199:0.000000:0.000000:0.000000 las primitivas de ( ) son las :@0.082546:0.313444:0.245456:0.313444:0.245456:0.300588:0.082546:0.300588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.180952:0.313444:0.194762:0.313444:0.194762:0.300815:0.180952:0.300815:0.000000:0.000000:0.000000 funciones derivables ( ), :@0.082546:0.327060:0.234251:0.327060:0.234251:0.314204:0.082546:0.314204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F x:@0.207910:0.327060:0.224461:0.327060:0.224461:0.314431:0.207910:0.314431:0.000000:0.000000:0.000000 tales que :@0.082546:0.340676:0.139731:0.340676:0.139731:0.327820:0.082546:0.327820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F x:@0.137683:0.357866:0.157442:0.357866:0.157442:0.345237:0.137683:0.345237:0.000000:0.000000:0.000000 '( ) ( ).:@0.144806:0.357866:0.200545:0.357866:0.200545:0.345010:0.144806:0.345010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.164536:0.357412:0.177081:0.357412:0.177081:0.346190:0.164536:0.346190:0.000000 f x:@0.180244:0.357866:0.194054:0.357866:0.194054:0.345237:0.180244:0.345237:0.000000:0.000000:0.000000 La :@0.082531:0.375057:0.098992:0.375057:0.098992:0.362201:0.082531:0.362201:0.000000:0.000000:0.000000 integral indefinida:@0.098766:0.375057:0.209884:0.375057:0.209884:0.361418:0.098766:0.361418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es :@0.209612:0.375057:0.228708:0.375057:0.228708:0.362201:0.209612:0.362201:0.000000:0.000000:0.000000:0.000000 el conjunto de las infinitas :@0.082531:0.388673:0.236278:0.388673:0.236278:0.375817:0.082531:0.375817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 primitivas que puede tener :@0.082531:0.402289:0.243260:0.402289:0.243260:0.389433:0.082531:0.389433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una función.:@0.082531:0.415905:0.155002:0.415905:0.155002:0.403049:0.082531:0.403049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Por ejemplo, la ecuación::@0.082531:0.433095:0.230082:0.433095:0.230082:0.420239:0.082531:0.420239:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y ( ) admite infinitas:@0.082531:0.450285:0.244621:0.450285:0.244621:0.437429:0.082531:0.437429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.092321:0.449831:0.104866:0.449831:0.104866:0.438609:0.092321:0.438609:0.000000 e:@0.108029:0.450762:0.115559:0.450762:0.115559:0.436317:0.108029:0.436317:0.000000 f x dx:@0.115484:0.450285:0.146779:0.450285:0.146779:0.437656:0.115484:0.437656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 soluciones que difieren en :@0.082531:0.467475:0.242136:0.467475:0.242136:0.454620:0.082531:0.454620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una constante. Esto significa :@0.082531:0.481091:0.253159:0.481091:0.253159:0.468236:0.082531:0.468236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que las gráficas de dos :@0.082531:0.494708:0.219741:0.494708:0.219741:0.481852:0.082531:0.481852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 primitivas cualesquiera de :@0.082531:0.508324:0.240523:0.508324:0.240523:0.495468:0.082531:0.495468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.082531:0.521940:0.086372:0.521940:0.086372:0.509311:0.082531:0.509311:0.000000 son traslaciones verticales :@0.086311:0.521940:0.246332:0.521940:0.246332:0.509084:0.086311:0.509084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una de la otra. :@0.082531:0.535556:0.169807:0.535556:0.169807:0.522700:0.082531:0.522700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Por ejemplo,:@0.082531:0.549172:0.156813:0.549172:0.156813:0.536316:0.082531:0.536316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.082576:0.566044:0.088011:0.566044:0.088011:0.554819:0.082576:0.554819:0.000000 (3 1) ,:@0.087957:0.566044:0.250129:0.566044:0.250129:0.554617:0.087957:0.554617:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.090836:0.565641:0.101987:0.565641:0.101987:0.555666:0.090836:0.555666:0.000000 e:@0.107663:0.566468:0.114357:0.566468:0.114357:0.553628:0.107663:0.553628:0.000000 f x:@0.114290:0.566044:0.133032:0.566044:0.133032:0.554819:0.114290:0.554819:0.000000:0.000000:0.000000 2:@0.132995:0.561634:0.136803:0.561634:0.136803:0.554972:0.132995:0.554972:0.000000 2:@0.139648:0.565641:0.150800:0.565641:0.150800:0.555666:0.139648:0.555666:0.000000 dx:@0.163571:0.566044:0.175673:0.566044:0.175673:0.554819:0.163571:0.554819:0.000000:0.000000 5:@0.178511:0.565641:0.189662:0.565641:0.189662:0.555666:0.178511:0.555666:0.000000 x:@0.192474:0.566044:0.197896:0.566044:0.197896:0.554819:0.192474:0.554819:0.000000 3:@0.197825:0.561634:0.201634:0.561634:0.201634:0.554972:0.197825:0.554972:0.000000 2 1:@0.204479:0.565641:0.237839:0.565641:0.237839:0.555666:0.204479:0.555666:0.000000:0.000000:0.000000 x:@0.218441:0.566044:0.223863:0.566044:0.223863:0.554819:0.218441:0.554819:0.000000 C:@0.240651:0.566044:0.247853:0.566044:0.247853:0.554819:0.240651:0.554819:0.000000 válida para diversos valores :@0.082576:0.583548:0.246663:0.583548:0.246663:0.570693:0.082576:0.570693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 enteros de la constante . :@0.082576:0.597164:0.238677:0.597164:0.238677:0.584309:0.082576:0.584309:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.224716:0.597164:0.232819:0.597164:0.232819:0.584536:0.224716:0.584536:0.000000 Cada una de las primitivas es :@0.082576:0.610781:0.256587:0.610781:0.256587:0.597925:0.082576:0.597925:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la solución de la ecuación :@0.082576:0.624397:0.238693:0.624397:0.238693:0.611541:0.082576:0.611541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 df:@0.129844:0.647788:0.143162:0.647788:0.143162:0.633055:0.129844:0.633055:0.000000:0.000000 dx:@0.128526:0.662746:0.144480:0.662746:0.144480:0.648013:0.128526:0.648013:0.000000:0.000000 3 1.:@0.145099:0.653295:0.210464:0.653295:0.210464:0.640440:0.145099:0.640440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.148337:0.652842:0.160882:0.652842:0.160882:0.641620:0.148337:0.641620:0.000000 x:@0.171319:0.653295:0.177418:0.653295:0.177418:0.640666:0.171319:0.640666:0.000000 2:@0.177361:0.648334:0.181646:0.648334:0.181646:0.640839:0.177361:0.640839:0.000000 2:@0.184846:0.652842:0.197392:0.652842:0.197392:0.641620:0.184846:0.641620:0.000000 1:@0.140550:0.750028:0.145321:0.750028:0.145321:0.741683:0.140550:0.741683:0.000000 0:@0.145825:0.773977:0.151277:0.773977:0.151277:0.764440:0.145825:0.764440:0.000000 2:@0.135823:0.785608:0.143966:0.785608:0.143966:0.778324:0.135823:0.778324:0.000000 1:@0.143966:0.785902:0.148736:0.785902:0.148736:0.777558:0.143966:0.777558:0.000000 2:@0.135823:0.803571:0.143966:0.803571:0.143966:0.796287:0.135823:0.796287:0.000000 2:@0.143966:0.803865:0.148736:0.803865:0.148736:0.795521:0.143966:0.795521:0.000000 2:@0.135823:0.821534:0.143966:0.821534:0.143966:0.814250:0.135823:0.814250:0.000000 3:@0.143966:0.821828:0.148736:0.821828:0.148736:0.813484:0.143966:0.813484:0.000000 2:@0.135823:0.839497:0.143966:0.839497:0.143966:0.832213:0.135823:0.832213:0.000000 4:@0.143966:0.839791:0.148736:0.839791:0.148736:0.831447:0.143966:0.831447:0.000000 c:@0.162676:0.695539:0.167904:0.695539:0.167904:0.685000:0.162676:0.685000:0.000000 4:@0.167276:0.695539:0.187498:0.695539:0.187498:0.684810:0.167276:0.684810:0.000000:0.000000:0.000000:0.000000 5:@0.169400:0.695160:0.179869:0.695160:0.179869:0.685795:0.169400:0.685795:0.000000 c:@0.162286:0.714032:0.167515:0.714032:0.167515:0.703493:0.162286:0.703493:0.000000 3:@0.166886:0.714032:0.187109:0.714032:0.187109:0.703304:0.166886:0.703304:0.000000:0.000000:0.000000:0.000000 5:@0.169010:0.713653:0.179480:0.713653:0.179480:0.704288:0.169010:0.704288:0.000000 c:@0.162311:0.733046:0.167540:0.733046:0.167540:0.722507:0.162311:0.722507:0.000000 2:@0.166911:0.733046:0.187134:0.733046:0.187134:0.722318:0.166911:0.722318:0.000000:0.000000:0.000000:0.000000 5:@0.169035:0.732667:0.179505:0.732667:0.179505:0.723303:0.169035:0.723303:0.000000 c:@0.162098:0.750858:0.167326:0.750858:0.167326:0.740319:0.162098:0.740319:0.000000 1:@0.166698:0.750858:0.186920:0.750858:0.186920:0.740129:0.166698:0.740129:0.000000:0.000000:0.000000:0.000000 5:@0.168822:0.750479:0.179291:0.750479:0.179291:0.741114:0.168822:0.741114:0.000000 c:@0.162261:0.768452:0.167489:0.768452:0.167489:0.757912:0.162261:0.757912:0.000000 0:@0.166861:0.768452:0.187084:0.768452:0.187084:0.757723:0.166861:0.757723:0.000000:0.000000:0.000000:0.000000 5:@0.168985:0.768073:0.179455:0.768073:0.179455:0.758708:0.168985:0.758708:0.000000 c:@0.159370:0.797020:0.164599:0.797020:0.164599:0.786481:0.159370:0.786481:0.000000 1:@0.163970:0.797020:0.194034:0.797020:0.194034:0.786292:0.163970:0.786292:0.000000:0.000000:0.000000:0.000000:0.000000 52:@0.166094:0.796641:0.188529:0.796641:0.188529:0.787276:0.166094:0.787276:0.000000:0.000000 c:@0.159219:0.815125:0.164448:0.815125:0.164448:0.804586:0.159219:0.804586:0.000000 2:@0.163820:0.815125:0.193883:0.815125:0.193883:0.804397:0.163820:0.804397:0.000000:0.000000:0.000000:0.000000:0.000000 52:@0.165944:0.814747:0.188378:0.814747:0.188378:0.805382:0.165944:0.805382:0.000000:0.000000 c:@0.159345:0.834357:0.164574:0.834357:0.164574:0.823818:0.159345:0.823818:0.000000 3:@0.163945:0.834357:0.194009:0.834357:0.194009:0.823629:0.163945:0.823629:0.000000:0.000000:0.000000:0.000000:0.000000 52:@0.166069:0.833979:0.188504:0.833979:0.188504:0.824613:0.166069:0.824613:0.000000:0.000000 c:@0.164247:0.854640:0.169475:0.854640:0.169475:0.844101:0.164247:0.844101:0.000000 4:@0.168847:0.854640:0.198911:0.854640:0.198911:0.843912:0.168847:0.843912:0.000000:0.000000:0.000000:0.000000:0.000000 52:@0.170971:0.854262:0.193406:0.854262:0.193406:0.844896:0.170971:0.844896:0.000000:0.000000 2:@0.140550:0.731219:0.145321:0.731219:0.145321:0.722874:0.140550:0.722874:0.000000 3:@0.140550:0.712409:0.145321:0.712409:0.145321:0.704064:0.140550:0.704064:0.000000 4:@0.140550:0.693599:0.145321:0.693599:0.145321:0.685255:0.140550:0.685255:0.000000 1:@0.187536:0.776367:0.192306:0.776367:0.192306:0.768023:0.187536:0.768023:0.000000 2:@0.119056:0.776073:0.127199:0.776073:0.127199:0.768789:0.119056:0.768789:0.000000 1:@0.126955:0.776367:0.131725:0.776367:0.131725:0.768023:0.126955:0.768023:0.000000 2:@0.219792:0.776367:0.224563:0.776367:0.224563:0.768023:0.219792:0.768023:0.000000 y:@0.143992:0.682241:0.149830:0.682241:0.149830:0.670916:0.143992:0.670916:0.000000 x:@0.243254:0.777356:0.248946:0.777356:0.248946:0.766032:0.243254:0.766032:0.000000 f x:@0.161156:0.865686:0.172782:0.865686:0.172782:0.855147:0.161156:0.855147:0.000000:0.000000:0.000000 ( ) :@0.164361:0.865686:0.237676:0.865686:0.237676:0.854958:0.164361:0.854958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.178840:0.865308:0.189310:0.865308:0.189310:0.855943:0.178840:0.855943:0.000000 x:@0.192037:0.865686:0.197127:0.865686:0.197127:0.855147:0.192037:0.855147:0.000000 2:@0.197138:0.861545:0.200713:0.861545:0.200713:0.855290:0.197138:0.855290:0.000000 2 1:@0.203439:0.865308:0.234923:0.865308:0.234923:0.855943:0.203439:0.855943:0.000000:0.000000:0.000000 x:@0.216636:0.865686:0.221726:0.865686:0.221726:0.855147:0.216636:0.855147:0.000000 c:@0.237651:0.865686:0.242879:0.865686:0.242879:0.855147:0.237651:0.855147:0.000000 Tomado de: :@0.201097:0.882876:0.258283:0.882876:0.258283:0.872877:0.201097:0.872877:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 http://www.cfm.cl/~rjimenez/:@0.116453:0.893466:0.255821:0.893466:0.255821:0.883467:0.116453:0.883467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 bioingenieria/cap4.pdf:@0.150376:0.904056:0.255807:0.904056:0.255807:0.894057:0.150376:0.894057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.078581:0.145303:0.187141:0.145303:0.187141:0.128356:0.078581:0.128356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.161945:0.176057:0.161945:0.176057:0.144998:0.078581:0.144998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A esta derivada se la denota también como ( ), esto es, ( ) ( ). :@0.323781:0.143144:0.825710:0.143144:0.825710:0.127431:0.323781:0.127431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f' x:@0.642130:0.143144:0.662580:0.143144:0.662580:0.127708:0.642130:0.127708:0.000000:0.000000:0.000000:0.000000 df:@0.734236:0.135575:0.746736:0.135575:0.746736:0.121543:0.734236:0.121543:0.000000:0.000000 dx:@0.732881:0.151965:0.748075:0.151965:0.748075:0.137933:0.732881:0.137933:0.000000:0.000000 x:@0.757971:0.143144:0.765426:0.143144:0.765426:0.127708:0.757971:0.127708:0.000000 5:@0.774096:0.142589:0.789429:0.142589:0.789429:0.128873:0.774096:0.128873:0.000000 f' x:@0.793295:0.143144:0.813745:0.143144:0.813745:0.127708:0.793295:0.127708:0.000000:0.000000:0.000000:0.000000 Recuerda que esta derivada define una nueva función que es un polinomio :@0.323781:0.184402:0.874318:0.184402:0.874318:0.168689:0.323781:0.168689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de grado 1. :@0.323781:0.202680:0.428868:0.202680:0.428868:0.186967:0.323781:0.186967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.393526:0.202125:0.408859:0.202125:0.408859:0.188410:0.393526:0.188410:0.000000 2. Funciones polinomiales de grado 4:@0.293660:0.242047:0.607551:0.242047:0.607551:0.225377:0.293660:0.225377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.579038:0.241492:0.594371:0.241492:0.594371:0.227776:0.579038:0.227776:0.000000 p x:@0.459188:0.281418:0.480633:0.281418:0.480633:0.265983:0.459188:0.265983:0.000000:0.000000:0.000000 ( ) :@0.468373:0.281418:0.546117:0.281413:0.546117:0.265701:0.468373:0.265706:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.489302:0.280864:0.504636:0.280864:0.504636:0.267148:0.489302:0.267148:0.000000 a:@0.508501:0.281418:0.517760:0.281418:0.517760:0.265983:0.508501:0.265983:0.000000 0:@0.517696:0.284586:0.522933:0.284586:0.522933:0.275425:0.517696:0.275425:0.000000 1:@0.526845:0.280859:0.542178:0.280859:0.542178:0.267143:0.526845:0.267143:0.000000 a x:@0.546044:0.281413:0.567866:0.281413:0.567866:0.265978:0.546044:0.265978:0.000000:0.000000:0.000000 1:@0.555221:0.284586:0.560457:0.284586:0.560457:0.275425:0.555221:0.275425:0.000000 :@0.567793:0.281413:0.591023:0.281413:0.591023:0.265701:0.567793:0.265701:0.000000:0.000000:0.000000 1:@0.571750:0.280859:0.587083:0.280859:0.587083:0.267143:0.571750:0.267143:0.000000 a x:@0.590949:0.281413:0.612778:0.281413:0.612778:0.265978:0.590949:0.265978:0.000000:0.000000:0.000000 2:@0.600134:0.284586:0.605371:0.284586:0.605371:0.275425:0.600134:0.275425:0.000000 2:@0.612713:0.275349:0.617950:0.275349:0.617950:0.266189:0.612713:0.266189:0.000000 :@0.617902:0.281413:0.641132:0.281413:0.641132:0.265701:0.617902:0.265701:0.000000:0.000000:0.000000 1:@0.621860:0.280859:0.637193:0.280859:0.637193:0.267143:0.621860:0.267143:0.000000 a x:@0.641059:0.281413:0.662881:0.281413:0.662881:0.265978:0.641059:0.265978:0.000000:0.000000:0.000000 3:@0.650237:0.284586:0.655474:0.284586:0.655474:0.275425:0.650237:0.275425:0.000000 3:@0.662816:0.275349:0.668053:0.275349:0.668053:0.266189:0.662816:0.266189:0.000000 :@0.668005:0.281413:0.691235:0.281413:0.691235:0.265701:0.668005:0.265701:0.000000:0.000000:0.000000 1:@0.671963:0.280859:0.687296:0.280859:0.687296:0.267143:0.671963:0.267143:0.000000 a x:@0.691161:0.281413:0.712984:0.281413:0.712984:0.265978:0.691161:0.265978:0.000000:0.000000:0.000000 4:@0.700340:0.284586:0.705577:0.284586:0.705577:0.275425:0.700340:0.275425:0.000000 4:@0.712917:0.275349:0.718154:0.275349:0.718154:0.266189:0.712917:0.266189:0.000000 , :@0.718108:0.281413:0.733184:0.281413:0.733184:0.265701:0.718108:0.265701:0.000000:0.000000:0.000000:0.000000 ;:@0.733073:0.280859:0.745351:0.280859:0.745351:0.267143:0.733073:0.267143:0.000000 x:@0.745259:0.281413:0.752714:0.281413:0.752714:0.265978:0.745259:0.265978:0.000000 ,:@0.752640:0.281413:0.791513:0.281413:0.791513:0.265701:0.752640:0.265701:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.756606:0.281123:0.771242:0.281123:0.771242:0.267714:0.756606:0.267714:0.000000 R:@0.775112:0.280554:0.788402:0.280554:0.788402:0.267656:0.775112:0.267656:0.000000 siendo , , , , fijos. La derivada de es:@0.323784:0.320785:0.691334:0.320779:0.691334:0.305066:0.323784:0.305073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a a a a a:@0.376558:0.320785:0.471633:0.320779:0.471633:0.305344:0.376558:0.305350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.385752:0.323951:0.390988:0.323951:0.390988:0.314791:0.385752:0.314791:0.000000 1:@0.407206:0.323951:0.412443:0.323951:0.412443:0.314791:0.407206:0.314791:0.000000 2:@0.428662:0.323951:0.433899:0.323951:0.433899:0.314791:0.428662:0.314791:0.000000 3:@0.450117:0.323951:0.455354:0.323951:0.455354:0.314791:0.450117:0.314791:0.000000 4:@0.471571:0.323951:0.476808:0.323951:0.476808:0.314791:0.471571:0.314791:0.000000 [:@0.480711:0.320489:0.495348:0.320489:0.495348:0.307079:0.480711:0.307079:0.000000 R :@0.499217:0.319919:0.517017:0.319919:0.517017:0.307022:0.499217:0.307022:0.000000:0.000000 p:@0.662471:0.320779:0.671730:0.320779:0.671730:0.305344:0.662471:0.305344:0.000000 dp:@0.439436:0.352577:0.456086:0.352577:0.456086:0.338545:0.439436:0.338545:0.000000:0.000000 dx:@0.440155:0.368967:0.455349:0.368967:0.455349:0.354935:0.440155:0.354935:0.000000:0.000000 ( ) ( ) 2:@0.456502:0.360146:0.598670:0.360146:0.598670:0.344433:0.456502:0.344433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.465246:0.360146:0.472701:0.360146:0.472701:0.344710:0.465246:0.344710:0.000000 5:@0.481371:0.359591:0.496704:0.359591:0.496704:0.345875:0.481371:0.345875:0.000000 p' x:@0.500569:0.360146:0.524278:0.360146:0.524278:0.344710:0.500569:0.344710:0.000000:0.000000:0.000000:0.000000 5:@0.532948:0.359591:0.548281:0.359591:0.548281:0.345875:0.532948:0.345875:0.000000 a:@0.552146:0.360146:0.561405:0.360146:0.561405:0.344710:0.552146:0.344710:0.000000 1:@0.561340:0.363318:0.566577:0.363318:0.566577:0.354158:0.561340:0.354158:0.000000 1:@0.570488:0.359591:0.585822:0.359591:0.585822:0.345875:0.570488:0.345875:0.000000 a x:@0.598578:0.360146:0.620412:0.360146:0.620412:0.344710:0.598578:0.344710:0.000000:0.000000:0.000000 2:@0.607767:0.363318:0.613003:0.363318:0.613003:0.354158:0.607767:0.354158:0.000000 3:@0.620339:0.360146:0.652478:0.360146:0.652478:0.344433:0.620339:0.344433:0.000000:0.000000:0.000000:0.000000 1:@0.624296:0.359591:0.639629:0.359591:0.639629:0.345875:0.624296:0.345875:0.000000 a x:@0.652386:0.360146:0.674227:0.360146:0.674227:0.344710:0.652386:0.344710:0.000000:0.000000:0.000000 3:@0.661581:0.363318:0.666818:0.363318:0.666818:0.354158:0.661581:0.354158:0.000000 2:@0.674160:0.354082:0.679397:0.354082:0.679397:0.344921:0.674160:0.344921:0.000000 4:@0.679351:0.360146:0.711490:0.360146:0.711490:0.344433:0.679351:0.344433:0.000000:0.000000:0.000000:0.000000 1:@0.683308:0.359591:0.698641:0.359591:0.698641:0.345875:0.683308:0.345875:0.000000 a x:@0.711398:0.360146:0.733230:0.360146:0.733230:0.344710:0.711398:0.344710:0.000000:0.000000:0.000000 4:@0.720586:0.363318:0.725823:0.363318:0.725823:0.354158:0.720586:0.354158:0.000000 3:@0.733165:0.354082:0.738402:0.354082:0.738402:0.344921:0.733165:0.344921:0.000000 , :@0.738354:0.360146:0.753430:0.360146:0.753430:0.344433:0.738354:0.344433:0.000000:0.000000:0.000000:0.000000 ;:@0.753319:0.359591:0.765597:0.359591:0.765597:0.345875:0.753319:0.345875:0.000000 x:@0.765505:0.360146:0.772960:0.360146:0.772960:0.344710:0.765505:0.344710:0.000000 ,:@0.772886:0.360146:0.811759:0.360146:0.811759:0.344433:0.772886:0.344433:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.776852:0.359856:0.791488:0.359856:0.791488:0.346446:0.776852:0.346446:0.000000 R:@0.795358:0.359286:0.808648:0.359286:0.808648:0.346388:0.795358:0.346388:0.000000 que define una nueva función, o sea, un polinomio de grado 3.:@0.323783:0.399517:0.797714:0.399517:0.797714:0.383805:0.323783:0.383805:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.766404:0.398963:0.781737:0.398963:0.781737:0.385247:0.766404:0.385247:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000